Posted on 09/26/2022 3:05:10 PM PDT by BenLurkin
For even a modest number of electrons and cutting-edge computational approaches, the problem requires serious computing power. That's because when electrons interact, their fates can become quantum mechanically entangled: Even once they're far apart on different lattice sites, the two electrons can't be treated individually, so physicists must deal with all the electrons at once rather than one at a time. With more electrons, more entanglements crop up, making the computational challenge exponentially harder.
One way of studying a quantum system is by using what's called a renormalization group. That's a mathematical apparatus physicists use to look at how the behavior of a system—such as the Hubbard model—changes when scientists modify properties such as temperature or look at the properties on different scales. Unfortunately, a renormalization group that keeps track of all possible couplings between electrons and doesn't sacrifice anything can contain tens of thousands, hundreds of thousands or even millions of individual equations that need to be solved. On top of that, the equations are tricky: Each represents a pair of electrons interacting.
Di Sante and his colleagues wondered if they could use a machine learning tool known as a neural network to make the renormalization group more manageable. The neural network is like a cross between a frantic switchboard operator and survival-of-the-fittest evolution. First, the machine learning program creates connections within the full-size renormalization group. The neural network then tweaks the strengths of those connections until it finds a small set of equations that generates the same solution as the original, jumbo-size renormalization group. The program's output captured the Hubbard model's physics even with just four equations
(Excerpt) Read more at phys.org ...
ping
I was thinking about that solution the other day but I forgot to write it down. My bad.
Meh… copied from my 8th grade essay.
What a retard.
A neural network is a set of simultaneous non-linear equations with an infinite set of solution sets.
You approach a solution set by feeding a signal through the network and correcting it with the feedback from the error signal.
With each iteration the error gets smaller and smaller until you have a trained network that outputs the desired pattern from each input pattern.
My K&E is a prized possession. Mahogany with a chamois lined leather case.
And I forgot to carry the 2.
Nice. Mine is a prized possession too. Dark green leather case.
I'd sell my laptop before I'd sell my K&E — "… my cold dead hands".
“even with fresh batteries.”
LOL!!
Might they be Maxwell’s equations?
Meh, white man’s math.
What an achievement
Maff’s be racissss
The answer was 42.
Renormilization just allows mathemeticians to take advantage of what engineers rely on every day to come up with practical solutions.
“Don’t sweat the small stuff”.
Let us not forget -Heaviside.
< Artificial intelligence reduces a 100,000-equation quantum physics problem to only four equations <
That doesn’t help me at all. I can only solve three equations at a time.
Got one . Delrin?
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